Hidden Symmetry, Excitonic Transitions and Two-Dimensional Kane’s Exciton in the Quantum Well
نویسندگان
چکیده
The influence of hidden symmetry on two-dimensional excitonic states in semiconductor quantum wells is investigated. It is shown that excitonic states in quantum wells, with the parabolic dispersion law for the electron and hole, and Sommerfeld’s coefficients for excitonic transitions are determined only with the principle quantum number within the framework of two-dimensional Coulomb potential. This is a result of hidden symmetry of two-dimensional Coulomb problem, conditioned by the existence of two-dimensional analog of the Runge-Lentz vector. For the narrow gap semiconductor quantum well with the non-parabolic dispersion law of electron and hole, in the two-band Kane model, it is shown that two-dimensional excitonic states are described in the frames of analog of the Klein-Gordon equation with the two-dimensional Coulomb potential. Non-stability of the ground state of the two-dimensional Kane’s exciton investigated. c © Electronic Journal of Theoretical Physics. All rights reserved.
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